I have a F330, and as we all know it has no SDI. Now, what would the smartest/easiest/handiest solution to add and SDI-option to the camera, so that is's onboard all the time.

It could either be an external stuck-on thingie or some other creative solution. It would also be great to power the thingie from the camera,

Has anybody done this before? I know there are various mini converters out there, but it looks like they all use a separate power supply to work. I'm looking for a permanent solution that could sit on-cam all the time and we could just plug in a wire and get SDI with embedded audio out.

Yes, that's what I have found too. The external ones are mostly +5V and require their own power supply. Would have been nice it there were an option board to plug into the 330 making it compatible with 350 (I don't need the over-/undercrank feature) but that's probably a closed road.

So if anyone has heard of/tried a composite-to-SDI converter that is small enough to sit for example behind the battery, I would be more than interested...

A search on the web revealed 2 options: Datavideo has an analog-to-DVI converter to around USD 411, that will fit between the tripod and the camera - but fastened to the camera. This is a clever solution that's for the most are out of the way in daily use. It runs 12V, which can be taken from the D-tap on SONY cams.

However, I choose the mini-converter from Blackmagic, which also can be powered from the D-tap. However, this requires a couple of pieces of Velco to be mounted on the back of the battery. This is more convenient to me, as the cable routing will be very short from the Component out and up to the converter.
Price for this solution was GBP368 - approx. the same as the Datavideo converter, when the import duty is considered.

Both converters has embedded audio. So anyone with a F330 camera who want to have SDI out, but don't want to pay megabucks for the bigger model - there IS a solution :-)

did you make some tests? How is quality after going Component->HDSDI? Is the A/D conversion noisy?
How do you think does it hold up to other Full HD pics (the pdw330 does 1440x1080 stretched to 1920x1080)?

No tests yet - received the converter on Monday, but have had to make up a D-plug wire for supplying power from the cam to the converter (which came out nice, btw - the SONY's D-plug tap for a sungun is stabilized 12V, which the converter needs) - and now I'm waiting for 6 male BNC-plugs, so that I can make the 3 component wires (they will be approx. 5 cm in lenght, and I plan on collecting them in a single crimpflex sleeve so they will be permanently attached between the cam and the converter.

BTW - found out the converter would sit much better on the side of the camera (same side as the disc mecanism), as the component outputs are more or less below the converter, then. Also saves me getting the thing off when I change batteries. Velcro is a blessing :-)

Take a look at the Blackmagic Mini Converters. I've had the component to SDI version for a couple of years now on my F330 and I am quite happy with it. I built an audio/video harness for the cables, mount it on my Anton Bauer wireless plates and power it from the AB 12V power out. The picture is perfect and the unit is trouble free.